Outline Formal Modeling of Flexible Processes in Mobile Ad-hoc Networks with Algebraic Higher-Order Nets ◮ motivation and basic ideas ◮ example: emergency scenario ◮ nets and rules as token ◮ algebraic higher-order nets Institut f¨ ur Softwaretechnik und theoretische Informatik Technische Universit¨ at Berlin ◮ modeling workflows in MANET s ◮ conclusion May 2007 Modeling Workflows in Mobile Ad-hoc Networks Emergency Scenario: Archaeological Site after an Earthquake Hit Picture Store ◮ network of mobile devices Area ◮ team members communicate with one another via wireless links without relying on an underlying infrastructure Operator ◮ team members execute sets of activities modeled as workflows Movement needed to accomplish Precarious ◮ MANET s topology both influences and is influenced by the the task Museum Bell-Tower Building workflow ◮ modeling workflow modifications as required by topology Camera transformations Bridge Church requirements for the modeling technique Team Leader Movement needed to maintain the network connectivity; should be adaptively driven by the cooperative application Cooperation with MOBIDIS – Universit´ a di Roma ”La Sapienza” WORKPAD – EU-project (8 sites)
System Architecture Modeling Workflows and Transformations in MANET s Mobile Device Coordinator Mobile Device Coordinator Mobile Device Coordinator Mobile Device Coordinator Mobile Device i Mobile Device i Mobile Device i Mobile Device i Coordination Layer Coordination Layer Coordination Layer Coordination Layer Workflow Workflow Workflow Workflow Schema Schema Schema Schema Service 1 Service 1 Service 1 Service 1 Service 2 Service 2 Service 2 Service 2 Workflow Workflow Workflow Workflow ◮ applying algebraic approaches based on Workflow Workflow Workflow Workflow Execution Execution Execution Execution Adapter Adapter Adapter Adapter Engine Engine Engine Engine Network Service Interface Network Service Interface Network Service Interface Network Service Interface Rewriting Rewriting Rewriting Rewriting algebraic higher-order nets with Rules Rules Rules Rules Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Petri nets, graphs and rules as tokens Predictive Layer Predictive Layer Predictive Layer Predictive Layer ◮ algebraic higher-order net coordinates Mobile Device j Mobile Device j Mobile Device j Mobile Device j workflow execution and rule application Network Service Interface Network Service Interface Network Service Interface Network Service Interface Service 3 Service 3 Service 3 Service 3 Service 4 Service 4 Service 4 Service 4 ◮ a team consists of a workflow and its topology graph Network Service Interface Network Service Interface Network Service Interface Network Service Interface Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) Wireless Stack (802.11x, Bluetooth) ◮ rules are tuples of net and graph rules ◮ modeling at the coordination layer Workflow Workflow Rules Teams Adaption Execution ◮ modeling of the distributed workflows ◮ abstraction from the technical infrastructure Cooperation with MOBIDIS – Universit´ a di Roma ”La Sapienza” WORKPAD – EU-project (8 sites) Workflow Execution Workflow Execution fire ( s , t ) Workflow fire ( s , t ) Workflow Execution Execution Team Team s enabled ( s , t ) s enabled ( s , t ) = true = true signature and algebra for signature and algebra for ◮ Reconfigurable Petri ◮ Reconfigurable Petri PN1 PN1’ Start Start systems, i.e. systems, i.e. P/T-nets with markings P/T-nets with markings ◮ firing behavior ◮ firing behavior Compile Compile Select Building Select Building Questionnaire ◮ and net transformations Questionnaire ◮ and net transformation Go to Destination Go to Destination
Workflow Adaption Workflow Adaption L1 I1 R1 L1 I1 R1 Go to Destination Go to Destination Go to Destination Go to Destination Follow Team Member 3 Follow Team Member 3 Send Photos Send Photos signature and algebra for PN1 K1 PN2 Send Photos Send Photos ◮ Petri system rules Select Building Select Building Select Building ◮ transformation of systems Go to Destination Go to Destination Teams Workflow Adaption s Zoom on Zoom on Zoom on damaged part damaged part damaged part Rule Team r 1 ( cod . ( m 1 )) = s Follow Team Member 3 s ′ Capture Scene Capture Scene Capture Scene ∧ ( transform . ( r 1 , m 1 )) = s ′ SystemRules ∧ ( dom . ( c ′ )) = ( trans . ( s ′ )) Send Photos Send Photos Matching Matching Matching Formale Modellierung und Analyse flexibler Processe Main tasks of in mobilen ad-hoc Netzwerken 2006 – 2008 funded by the ◮ characterization of main properties http://tfs.cs.tu-berlin.de/formalnet/ ◮ suitable restriction of AHO nets ◮ MANET s: ◮ structuring and transformation in AHO nets research focus mainly on technical infrastructure ◮ process modeling and analysis in AHO nets in this project: modeling of workflows in the MANET s ◮ methodology and (prototypes of) tool support ◮ process modeling: various approaches, e.g. process algebras, activity-, flow-, or GOAL: state-charts, Petri nets, adaptive workflows, ... adequate specification technique for in this project: algebraic higher-order nets multi-level modeling of workflows in MANET s ◮ formal modeling and adaption of workflows in MANET s: in this project: reconfigurable Petri nets; Project Leaders: H. Ehrig, J. Padberg, K. Hoffmann
� � � � � � Reconfigurable P/T-systems P/T-systems Definition (P/T-systems PS = ( N , M 0 ) ) ◮ a net N = ( P , T , pre , post ) with ◮ a set of places P ◮ a set of transistions T ◮ algebraic approach to ◮ weighted arcs pre , post : T → P ⊕ Petri (net) systems ◮ the initial marking M 0 ∈ P ⊕ ◮ algebraic approach to ◮ P/T-morphism f = ( f P , f T ) : PS 1 → PS 2 net transformations with f P : P 1 → P 2 and f T : T 1 → T 2 s.t. ◮ based on ◮ f ⊕ P ◦ pre 1 = pre 2 ◦ f T and f ⊕ P ◦ post 1 = post 2 ◦ f T weak adhesive HLR systems ◮ f ⊕ P ( M 0 1 | p ) ≤ M 0 2 | f P ( p ) for p ∈ P 1 t ◮ firing PS = ( N , M ) − → ( N , M ′ ) = PS ′ where M [ t > M ′ in net N Rule application Concurrent situation firing steps Definition (Net transformation) (N0,M0) (N0,M0’) (N0,M0’) l r A rule rule = ( L ← − K − → R ) with P/T-systems L , K , and R , and Select Building Select Building Select Building l r two strict injections K − → L and K − → R Go to Destination Go to Destination Go to Destination m is applicable at match L − → PS 1 if the gluing condition holds rule leading to a direct transformation PS 1 = ⇒ PS 2 Make Photo Make Photo Make Photo − → − → consisting of the pushouts (1) and (2): l r L K R Send Photos Send Photos Send Photos m ( 1 ) ( 2 ) � PS 2 PS ′ PS 1 Matching Matching Matching 1
� � � � � � � � � � � � Concurrent situation Independence and conflict � ( N 1 , M ′ ( N 0 , M ′′′ 0 ) ( N 0 , M ′ 0 ) 1 ) rule 1 , m ′ t 2 1 ) transformation steps t 1 ( 1 ) t 1 ( 2 ) t 1 (N0,M0) (N1,M1) (N2,M2) ( N 0 , M ′′ 0 ) ( N 0 , M 0 ) ( N 1 , M 1 ) t 2 ( rule 1 , m 1 ) Select Building Select Building Select Building ( rule 2 , m ′ ( rule 2 , m ′′ 2 ) ( 3 ) ( rule 2 , m 2 ) ( 4 ) 2 ) Go to Destination Go to Destination Go to Destination � ( N 3 , M 3 ) ( N 2 , M ′ 2 ) ( N 2 , M 2 ) ( rule 1 , m ′′ t 2 1 ) Zoom on damaged part Follow Camera Follow Camera Device Device = ⇒ = ⇒ Make Photo Make Photo square (1) classical Petri net notion: conflict/conflict free Capture Scene square (4) classical graph transformation notion: parallel independence Send Photos Send Photos Send Photos square (2) new situation: parallel independence Matching Matching square (3) of transformation and firing step Matching Main results for square (2) and (3) Main Results for square (4) Definition (Parallel Independence) A transformation and a firing step are parallel independent if Theorem (1) the transition is not deleted by the transformation step and The category ( PTSys , M strict ) is a weak adhesive HLR category. (2) enough tokens are left by the firing step. Main results for weak adhesive HLR categories: Theorem 1. Local Church-Rosser Theorem, ( PN 0 , M 0 ) 2. Parallelism Theorem, � � � � �������� � � � � � � 3. Concurrency Theorem. � � � � Given parallel independent steps � ( PN 0 , M ′ 0 ) ( PN 1 , M 1 ) ( PN 0 , M 0 ) = ⇒ ( PN 1 , M 1 ) � � � � �������� and � � � � � � � � � � → ( PN 0 , M ′ � ( PN 0 , M 0 ) − 0 ) ( PN 1 , M ′ Main result in Petri Nets’07 paper 1 ) then the square is commuting Main result in Petri Nets’07 paper
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